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Metamath Proof Explorer

Theorem snexOLD

Description: Obsolete version of snex as of 6-Mar-2026. (Contributed by NM, 7-Aug-1994) (Revised by Mario Carneiro, 19-May-2013) (Proof modification is discouraged.) (New usage is discouraged.)

		Ref	Expression
	Assertion	snexOLD	⊢ { 𝐴 } ∈ V

Proof

Step	Hyp	Ref	Expression
1		snexg	⊢ ( 𝐴 ∈ V → { 𝐴 } ∈ V )
2		snprc	⊢ ( ¬ 𝐴 ∈ V ↔ { 𝐴 } = ∅ )
3	2	biimpi	⊢ ( ¬ 𝐴 ∈ V → { 𝐴 } = ∅ )
4		0ex	⊢ ∅ ∈ V
5	3 4	eqeltrdi	⊢ ( ¬ 𝐴 ∈ V → { 𝐴 } ∈ V )
6	1 5	pm2.61i	⊢ { 𝐴 } ∈ V